Results 11 to 20 of about 275 (133)
Duality theory for enriched Priestley spaces [PDF]
Journal of Pure and Applied Algebra, 2023 The term Stone-type duality often refers to a dual equivalence between a category of lattices or other partially ordered structures on one side and a category of topological structures on the other. This paper is part of a larger endeavour that aims to extend a web of Stone-type dualities from ordered to metric structures and, more generally, to ...
Hofmann, Dirk, Nora, Pedro
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Localic Priestley duality [PDF]
Journal of Pure and Applied Algebra, 1997 What is proved here is actually not a duality but a (covariant) equivalence: that between the localic analogues of the category of ordered Stone spaces (which were introduced by \textit{H. A. Priestley} in 1970 as the duals of distributive lattices) and of the category of coherent spaces (the non-Hausdorff generalization of Stone spaces which appeared ...
Townsend, Chris
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Priestley duality for some algebras with a negation operator [PDF]
Contributions to Discrete Mathematics, 2007 In \cite{Celani} it was introduced the variety of ¬-lattices as bounded distributive lattice A endowed with a unary operation ¬, satisfying the axioms ¬0≈1 and ¬(a∨b)≈¬a∧¬b. In this paper we shall apply the Priestley duality developed in \cite{Celani} to give a unified, short and self-contained Priestley duality for semi-De Morgan algebras, demi-p ...
Celani, Sergio A., Celani, Sergio Arturo
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Connecting generalized Priestley duality to Hofmann-Mislove-Stralka duality [PDF]
Theory and Applications of CategoriesWe connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other things, this involves consideration of various morphisms between algebraic frames. We also show how Stone duality for boolean algebras and generalized boolean algebras fits as a
G. Bezhanishvili +2 more
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Priestley-type dualities for partially ordered structures [PDF]
Annals of Pure and Applied Logic, 2016 44 ...
CARAMELLO, OLIVIA
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Priestley duality and representations of recurrent dynamics [PDF]
For an arbitrary dynamical system there is a strong relationship between global dynamics and the order structure of an appropriately constructed Priestley space. This connection provides an order-theoretic framework for studying global dynamics. In the classical setting, the chain recurrent set, introduced by C.
Kalies, William, Vandervorst, Robert
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A duality theoretic view on limits of finite structures: Extended version [PDF]
Logical Methods in Computer Science, 2022 A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of ...
Mai Gehrke, Tomáš Jakl, Luca Reggio
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Distributive lattices with strong endomorphism kernel property as direct sums [PDF]
Categories and General Algebraic Structures with Applications, 2020 Unbounded distributive lattices which have strong endomorphism kernel property (SEKP) introduced by Blyth and Silva in [3] were fully characterized in [11] using Priestley duality (see Theorem 2.8}). We shall determine the structure of special elements (
Jaroslav Gurican
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Incidence structures and Stone–Priestley duality [PDF]
Annals of Mathematics and Artificial Intelligence, 2007 We observe that if $R:=(I,ρ, J)$ is an incidence We observe that if $R:=(I,ρ, J)$ is an incidence structure, viewed as a matrix, then the topological closure of the set of columns is the Stone space of the Boolean algebra generated by the rows. As a consequence, we obtain that the topological closure of the collection of principal initial segments of a
Mohamed Bekkali +2 more
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Restricted Priestley Dualities and Discriminator Varieties [PDF]
Studia Logica, 2017 Anyone who has ever worked with a variety~$\boldsymbol{\mathscr{A}}$ of algebras with a reduct in the variety of bounded distributive lattices will know a restricted Priestley duality when they meet one---but until now there has been no abstract definition. Here we provide one.
Brian A. Davey, A. Gair
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